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POST UTME OAU 2023 Mathematics | Objective

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Question 1

Find the volume of the frustum of a cone with height $h$ and radii of the bases $r_1$ and $r_2$.

Correct A. \frac{1}{3}\pi h $ r_1^2 + r_2^2 + r_1 r_2 $

B. \frac{1}{3}\pi h $ r_1^2 + r_2^2 - r_1 r_2 $

C. \frac{1}{3}\pi h $ r_1^2 - r_2^2 + r_1 r_2 $

D. \frac{1}{3}\pi h $ r_1^2 - r_2^2 - r_1 r_2 $

Correct Answer: A

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Question 2

Solve the inequality \frac{x}{x+1} > 1.

Correct A. x > -1

B. x < -1

C. x > 1

D. x < 1

Correct Answer: A

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Question 3

Find the derivative of the function f(x) = \frac{1}{x^2 + 1} u\sing the chain rule.

Correct A. \frac{-2x}{$ x^2 + 1 $^2}

B. \frac{2x}{$ x^2 + 1 $^2}

C. \frac{x}{$ x^2 + 1 $^2}

D. \frac{-x}{$ x^2 + 1 $^2}

Correct Answer: A

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Question 4

Solve the system of equations \begin{align*} x + y &= 2 \ x - y &= 1 \end{align*} u\sing matrices.

Correct A. \begin{pmatrix} 1 \ 1 \end{pmatrix}

B. \begin{pmatrix} 1 \ -1 \end{pmatrix}

C. \begin{pmatrix} 2 \ 1 \end{pmatrix}

D. \begin{pmatrix} 2 \ -1 \end{pmatrix}

Correct Answer: A

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Question 5

Find the surface area of the sphere with radius $r$.

Correct A. 4\pi r^2

B. 2\pi r^2

C. \pi r^2

D. \frac{1}{2}\pi r^2

Correct Answer: A

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Question 6

In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?

A. 0.1587

B. 0.3413

C. 0.4772

Correct D. 0.6915

Correct Answer: D

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Question 7

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.

Correct A. ( f'(x) = -\frac{2x}{$ x^2 + 1 $^2} )

B. ( f'(x) = \frac{2x}{$ x^2 + 1 $^2} )

C. ( f'(x) = -\frac{2}{$ x^2 + 1 $^2} )

D. ( f'(x) = \frac{2}{$ x^2 + 1 $^2} )

Correct Answer: A

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Question 8

A rec\tangular solid has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the solid.

A. 30 cm^3

B. 40 cm^3

Correct C. 50 cm^3

D. 60 cm^3

Correct Answer: C

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Question 9

Solve the equation $ 2^x + 2^x = 100 $.

A. x = 4

Correct B. x = 5

C. x = 6

D. x = 7

Correct Answer: B

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Question 10

Find the equation of the circle with center $ -2, 3 $ and radius 4.

Correct A. $ x + 2 \ $^2 + $ y - 3 $^2 = 16 )

B. $ x - 2 \ $^2 + $ y + 3 $^2 = 16 )

C. $ x + 2 \ $^2 + $ y + 3 $^2 = 16 )

D. $ x - 2 \ $^2 + $ y - 3 $^2 = 16 )

Correct Answer: A

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Question 11

Determine the value of x in the equation $ \frac{1}{2}x + 5 = \frac{3}{4}x - 2 $.

Correct A. \frac{11}{4}

B. \frac{3}{2}

C. -\frac{1}{2}

D. -\frac{3}{4}

Correct Answer: A

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Question 12

A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:3, how many loaves of whole wheat bread are sold per day?

Correct A. 120

B. 150

C. 180

D. 200

Correct Answer: A

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Question 13

A box contains 12 red balls, 16 blue balls, and 4 green balls. If a ball is drawn at random, what is the probability that it is either red or blue?

Correct A. \frac{7}{12}

B. \frac{4}{5}

C. \frac{3}{4}

D. \frac{2}{3}

Correct Answer: A

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Question 14

In a geometric sequence, the first term is 2 and the common ratio is 3. What is the sum of the first 5 terms?

Correct A. \frac{243}{2}

B. \frac{243}{4}

C. \frac{243}{8}

D. \frac{243}{16}

Correct Answer: A

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Question 15

A polynomial function has a degree of 4 and has zeros at x = -2, x = 3, and x = 4. What is the factored form of the polynomial?

Correct A. $ x + 2 $$ x - 3 $$ x - 4 $$ x + 1 $

B. $ x + 2 $$ x - 3 $$ x - 4 $$ x - 1 $

C. $ x + 2 $$ x - 3 $$ x - 4 $$ x + 3 $

D. $ x + 2 $$ x - 3 $$ x - 4 $$ x - 2 $

Correct Answer: A

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Question 16

Let $ mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} $ and $ mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} $. Find the vector $ mathbf{a} \times mathbf{b} $ u\sing the determinant formula.

Correct A. $ egin{pmatrix} 6 \ -2 \end{pmatrix} $

B. $ egin{pmatrix} -6 \ 2 \end{pmatrix} $

C. $ egin{pmatrix} 2 \ -6 \end{pmatrix} $

D. $ egin{pmatrix} -2 \ 6 \end{pmatrix} $

Correct Answer: A

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Question 17

Solve the equation $ x^3 + 2x^2 - 7x - 12 = 0 $ by factoring.

Correct A. $ x = -3, 2, -2 $

B. $ x = -3, 2, 4 $

C. $ x = -3, 2, -4 $

D. $ x = -3, 2, 1 $

Correct Answer: A

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Question 18

Find the value of $ \sin 2\theta $ given that $ \sin \theta = \frac{3}{5} $ and $ \cos \theta = \frac{4}{5} $.

Correct A. $ \frac{24}{25} $

B. $ \frac{12}{25} $

C. $ \frac{16}{25} $

D. $ \frac{20}{25} $

Correct Answer: A

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Question 19

Solve the inequality $ \frac{x + 2}{x - 1} > 0 $ u\sing a sign chart.

Correct A. $ x < -2 $ or $ x > 1 $

B. $ x < -2 $ or $ x < 1 $

C. $ x > -2 $ or $ x > 1 $

D. $ x < -2 $ or $ x < 1 $

Correct Answer: A

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Question 20

Find the value of $ \log_{10} \( x^2 \ $ ) given that $ \log_{10} x = 2 $.

Correct A. ( 4 )

B. ( 2 )

C. ( 1 )

D. ( 3 )

Correct Answer: A

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Question 21

Find the determinant of the matrix $ egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} $.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 22

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. 72

B. 80

C. 90

D. 100

Correct Answer: A

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Question 23

Solve the quadratic equation $ x^2 + 4x + 4 = 0 $.

A. -1

B. 0

C. 1

Correct D. -2

Correct Answer: D

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Question 24

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?

A. 0.2

Correct B. 0.25

C. 0.3

D. 0.4

Correct Answer: B

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Question 25

A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. 1500

Correct B. 2000

C. 2500

D. 3000

Correct Answer: B

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